Nonlinear Finite Element Analysis of RC Structures Incorporating Corrosion Effects

This paper presents the mathematical modeling techniques for nonlinear finite element analysis of RC structure to incorporate uniform corrosion effects. Effect of corrosion has been simulated as reduction in effective cross-sectional area of reinforcing bar, reduction in bonding phenomena and as reduction in material properties of reinforcing bar such as yield strength and elastic modulus. Appropriate constitutive laws for (i) corroded rebar elements and (ii) bond slip with corroded bar have been described. Procedure has been outlined to determine the global damage indicator by secant stiffness based approach. A corroded RC beam has been analysed to validate the proposed model and results have been compared with experimental response. A RC chimney has been analysed by considering the uniform corrosion effects. The result of corroded chimney shows the growth of damage with respect to increase in age of the structure. The results will give an insight for the maintenance and repair measures to be taken during the service life.     

A Generalized Finite Element Method for polycrystals with discontinuous grain boundaries

We present a Generalized Finite Element Method for the analysis of polycrystals with explicit treatment of grain boundaries. Grain boundaries and junctions, understood as loci of possible displacement discontinuity, are inserted into finite elements by exploiting the partition of unity property of finite element shape functions. Consequently, the finite element mesh does not need to conform to the polycrystal topology. The formulation is outlined and a numerical example is presented to demonstrate the potential and accuracy of the approach. The proposed methodology can also be used for branched and intersecting cohesive cracks, and comparisons are made to a related approach (Int. J. Numer. Meth. Engng. 2000; 48 :1741). Copyright © 2006 John Wiley & Sons, Ltd.     

Eigenvalue Analysis of MEMS Components with Multi-defect using Infinite Element Method Algorithm

Manufacturing defects in the membrane of MEMS (Micro-Electro-Mechanical-Systems) structures have a significant effect on the sensitivity and working range of the device. Thus, in optimizing the design of MEMS devices, it is essential that the effects of membrane defects (e.g., cracks) can be predicted in advance. Accordingly, this study proposes the detailed two-dimensional Infinite Element Method (IEM) formulation with Infinite Element (IE)-Finite Element (FE) coupling scheme for analyzing the out-of-plane vibration of isotropic MEMS membranes containing one or more tip cracks. In the proposed approach, a degenerative computation scheme is used to condense the multiple element layers of the IEM domain to a single layer with master nodes at the boundary only. The validity of the proposed algorithm is demonstrated by comparing the results obtained for the vibration of a rectangular membrane with the analytical solutions and the solutions obtained using the conventional Finite Element (FE) method, respectively. The validated IEM algorithm is then coupled with an FE scheme to analyze various cracked membrane vibration problems. The results show that the fundamental frequency of the membrane changes in accordance with the membrane thickness, but is unaffected by the number of cracks. However, it is shown that a change in the location of the cracks may cause a shift or rotation of the wave peaks of the structural mode shape. In general, the IEM algorithm presented in this paper provides a fast modeling, direct, and accurate tool to simulate the effects of cracks on the dynamic response of MEMS membranes. Furthermore, the algorithm can be easily integrated with experimental methods in order to test for the presence of cracks as part of the MEMS membrane quality control process.     

Three-dimensional Finite Element Buckling Analysis of Honeycomb Sandwich Composite Shells with Cutouts

This paper investigates the buckling response of honeycomb sandwich composite shells with cutouts under axial compression. The Wilson's incompatible solid Finite Element (FE) is used around cutouts to obtain the detail stress distribution there. While to reduce the computational expense, a special multilayered relative degrees-of-freedom (DOF) shell FE is used to model the regions far from the cutouts. The efficiency and accuracy of this modeling scheme are illustrated by two benchmarks. Then parametric studies are carried out to reveal how the buckling response is influenced by the area, the shape and the orientation of cutouts.     

A promising way to model cracks in composite using Discrete Element Method

In this article, the Discrete Element Method (DEM) is taking advantage for the damage modeling of a composite material. At this stage of work, a Representative Elementary Volume (REV) of an unidirectional composite material modeled in 3D is considered to prove the relevance of the approach. The interest to introduce the Discrete Elements (DE) on the scale of constituents (fiber and matrix) is to be able to report local mechanisms of degradation such as the matrix micro-fissuring, the fiber/matrix debonding and the break of fiber, appropriate to this type of material. The short-term objective is to use this DEM modeling to treat locally the damages induced by an impact loading associated with a conventional Finite Element modeling beyond the damaged zone. First, the geometrical modelings of the fiber and the matrix are presented. The phase of calibration of the DE model intrinsic parameters governing the fiber and matrix behavior and the fiber/matrix interface is afterward retailed. At this stage, each constituent is assumed to be brittle elastic. Then, simulations of longitudinal and transversal tensions but also of in plane and out of plane shearing are performed on the REV using DEM. The results are discussed and compared with those known for the literature. The capacity of the present DEM to capture the crack paths is particularly highlighted.     

Fatigue Fracture of a Cast Inconel 718 by Compression Loading and Its Verification by Finite Element Analysis (FEA)

Two out of three struts of a drilling tool’s 6.75″ Flow Diverter failed during operation. This failure resulted in invasion of mud into the electronic module of the tool. During drilling, high stick slip was observed. Measurement While Drilling (MWD) signal was good and Logging While Drilling (LWD) data was used to pick the oil/water contact point. At the end of the run, cracks were observed on the radii of the struts. Failure investigations were performed to identify the cause of the cracks. Material characterization, microstructural examinations, and fractography by SEM technique revealed that fatigue under compression forces was the cause of the cracking of the struts. Finite elemental analysis (FEA) was also used to determine the magnitude and the area of stress concentration. Failure mechanism has been explained. A few issues related to integrity of the material have also been raised.     

Fracture Analysis of Concrete Structural Components Accounting for Tension Softening Effect

This paper presents methodologies for fracture analysis of concrete structural components with and without considering tension softening effect. Stress intensity factor (SIF) is computed by using analytical approach and finite element analysis. In the analytical approach, SIF accounting for tension softening effect has been obtained as the difference of SIF obtained using linear elastic fracture mechanics (LEFM) principles and SIF due to closing pressure. Superposition principle has been used by accounting for non-linearity in incremental form. SIF due to crack closing force applied on the effective crack face inside the process zone has been computed using Green's function approach. In finite element analysis, the domain integral method has been used for computation of SIF. The domain integral method is used to calculate the strain energy release rate and SIF when a crack grows. Numerical studies have been conducted on notched 3-point bending concrete specimen with and without considering the cohesive stresses. It is observed from the studies that SIF obtained from the finite element analysis with and without considering the cohesive stresses is in good agreement with the corresponding analytical value. The effect of cohesive stress on SIF decreases with increase of crack length. Further, studies have been conducted on geometrically similar structures and observed that (i) the effect of cohesive stress on SIF is significant with increase of load for a particular crack length and (iii) SIF values decreases with increase of tensile strength for a particular crack length and load.     

A novel modeling to predict the critical current behavior of Nb3Sn PIT strand under transverse load based on a scaling law and Finite Element Analysis

Superconducting Nb₃Sn Powder-In-Tube (PIT) strands could be used for the superconducting magnets of the next generation Large Hadron Collider. The strands are cabled into the typical flat Rutherford cable configuration. During the assembly of a magnet and its operation the strands experience not only longitudinal but also transverse load due to the pre-compression applied during the assembly and the Lorentz load felt when the magnets are energized. To properly design the magnets and guarantee their safe operation, mechanical load effects on the strand superconducting properties are studied extensively; particularly, many scaling laws based on tensile load experiments have been established to predict the critical current dependence on strain. However, the dependence of the superconducting properties on transverse load has not been extensively studied so far. One of the reasons is that transverse loading experiments are difficult to conduct due to the small diameter of the strand (about 1 mm) and the data currently available do not follow a common measurement standard making the comparison between different data sets difficult. Recently at the University of Geneva, a new device has been developed to characterize the critical current of Nb₃Sn strands under transverse loads. In this work we present a new 2D Finite Element Analysis (FEA) to predict the electro-mechanical response of a PIT strand that was tested at the University of Geneva when transverse load is applied. The FEA provides the strain map for the superconducting filaments when the load is applied. Those strain maps are then used to evaluate the critical current behavior of a PIT strand using a recently developed scaling law that correlates the superconducting properties of a wire with the strain invariants due to the load applied on the superconductor. The benefits and limitations of this method are discussed based on the comparison between the critical current simulation results obtained with the filament strain map and the experimental results available for PIT strands.     

Prediction of fretting fatigue crack initiation in double lap bolted joint using Continuum Damage Mechanics

In fretting fatigue, the combination of small oscillatory motion, normal pressure and cyclic axial loading develops a noticeable stress concentration at the contact zone leading to accumulation of damage in fretted region, which produces micro cracks, and consequently forms a leading crack that can lead to failure. In fretting fatigue experiments, it is very difficult to detect the crack initiation phase. Damages and cracks are always hidden between the counterpart surfaces. Therefore, numerical modeling techniques for analyzing fretting fatigue crack initiation provide a precious tool to study this phenomenon. This article gives an insight in fretting fatigue crack initiation. This is done by means of an experimental set up and numerical models developed with the Finite Element Analysis (FEA) software package ABAQUS. Using Continuum Damage Mechanics (CDM) approach in conjunction with FEA, an uncoupled damage evolution law is used to model fretting fatigue crack initiation lifetime of Double Bolted Lap Joint (DBLJ). The predicted fatigue lifetimes are in good agreement with the experimentally measured ones. This comparison provides insight to the contribution of damage initiation and crack propagation in the total fatigue lifetime of DBLJ test specimens.     

A systematic approach for Integrated Computer-Aided Design and Finite Element Analysis of Functionally-Graded-Material objects

Computer-Aided Design (CAD) and Finite Element Analysis (FEA) of Functionally-Graded-Material (FGM) objects are generally regarded as separate domains of interest in CAD and Computer-Aided Engineering (CAE) community. Such a separation of CAD modeling and FEA of FGM objects makes it cumbersome and tedious for both designers and engineers to exchange the necessary information in the entire design process. Without appropriate CAD models, complex material distributions can hardly be represented and the FGM objects under examination remain simple in material variations (e.g. unidirectional gradations). With CAD modeling tools only, the end users are still uncertain whether or not the designed objects can really meet the functional requirements in terms of structural, thermal or other prescribed properties. This paper proposes a systematic approach to integrate these domain-dependent design tools in FGM object design. Integrated solutions to CAD modeling and property analysis of FGM objects are utilized to design complicated (bi-directional or even tri-variate) FGM objects. Complex FGM distributions are encoded into the proposed Heterogeneous Feature Tree (HFT) structure; and the material compositions of a given point of interest are interrogated from the CAD models at runtime. Integrated FEA of FGM objects are then carried out by establishing a link between the proposed CAD modeler (CAD4D) and a commercial FEA package (COMSOL Multiphysics). Four different (three unidirectional and one bidirectional) FGM objects are modeled with traditional analytic function based approaches and the proposed methods. Under the same thermal and mechanical conditions, the properties of each model are compared in terms of temperature fields, residual thermal stresses and the strain energy densities. Results show that the proposed approach can facilitate the design of complex FGM objects in a systematic way.     

Application of the Texture Component Crystal Plasticity Finite Element Method for Deep Drawing Simulations—A Comparison with Hill’s Yield Criterion

The Texture Component Crystal Plasticity FEM has the potential to improve the simulation of forming processes for crystalline materials. In this report it is applied to the deep drawing process. The resulting earing profiles are compared with results obtained by use of Hill’s potential from 1948 as well as with experimental data. It turns out that for simple cases both methods perform about equally good while for more complex ones the TCCP‐FEM is superior.     

Elasto-plastic Analysis of Two-dimensional Orthotropic Bodies with the Boundary Element Method

The Boundary Element Method (BEM) is introduced to analyze the elasto-plastic problems of 2-D orthotropic bodies. With the help of known boundary integral equations and fundamental solutions, a numerical scheme for elasto-plastic analysis of 2-D orthotropic problems with the BEM is developed. The Hill orthotropic yield criterion is adopted in the plastic analysis. The initial stress method and tangent predictor-radial return algorithm are used to determine the stress state in solving the nonlinear equation with the incremental iteration method. Finally, numerical examples show that the BEM is effective and reliable in analyzing elasto-plastic problems of orthotropic bodies.     

Three dimensional elasticity solution for static and dynamic analysis of multi-directional functionally graded thick sector plates with general boundary conditions

In this study, the three dimensional static and dynamic behavior of a thick sector plate made of two-directional functionally graded materials (2D-FGMs) is investigated. Material properties are assumed to be graded in both radial and thickness directions according to a simple power law distribution in terms of the volume fractions of the constituents. The governing equations are based on the 3D theory of elasticity. Employing 3D graded finite element method (GFEM) based on the Hamilton’s principle and Rayleigh–Ritz energy method, the equations are solved in space and time domains. In the case of static analysis, the sector plate is subjected to a uniform pressure load and for dynamic analysis is subjected to an impact loading. The effects of material gradient index, boundary condition and thickness to radius ratio of the sector plate on the static and dynamic responses are presented and discussed.     

空间相机主镜加工状态下的有限元分析

采用轻量化结构的空间相机主镜,因为镜体力学分布较传统的实心镜体复杂得多,因而轻型镜面的加工较之实心镜面复杂得多。镜子在加工中的支撑方式和受力状态是影响镜面加工精度的主要因素之一,没有严格准确的数学分析难以保证镜子的加工精度,本文用有限元法首次对正在加工中的空间相机主镜进行力学分析,根据变形规律设计了几种支撑方案,从中选定了主镜的最终支撑结构。镜面面形的加工精度实现PV值λ／10,MS值λ／62。满足使用要求。     

Influence of the hydrophobic force model on the capture of particles by bubbles: A computational study using Discrete Element Method

Discrete Element Method computer simulations have been carried out to analyse the influence of the hydrophobic force model on the capture of particles by a central bubble. Two hundred particles, with diameters ranging between 24 and 66 μm, were randomly positioned within a maximum distance from the surface of a bubble of 2 mm in diameter. Initial particle velocities were random in direction and value and they followed Gaussian distributions with standard deviations between 0.0 and 1.0 m/s. Three possible models, named A, B and C have been used in the simulations. The models correspond to different published relationships of the hydrophobic force with the distance between particle and bubble surfaces, d. Model A corresponds to a hydrophobic force that decays in the form 1/d; the hydrophobic force given by Model B uses a relationship in the form 1/d²; Model C predicts a force that decays in an exponential way in the form exp(?d/λ). These models have also been compared with a base case in which the hydrophobic force only acted when the particles were in contact with the bubble. Therefore, we could better discern between the influence of the initial particle velocities and the long range component of the hydrophobic force. The differences in the capture efficiency of the particles predicted by the three models were drastic. All particles were captured by the bubble in the cases simulated using Model A for any particle–bubble surface distance smaller than 1 mm. However, only 40% and 60% of the particles were captured even for particles located at distances of less than 50 μm from the bubble surface in the cases simulated using Models B and C (λ = 1 μm), respectively. In fact, the capture of particles seems to be more strongly influenced by how the hydrophobic force decays with interparticle distance in the range of tens of micrometres rather than by the differences between the models in the range of micrometres. Therefore, this work should aid in the future determination of a general hydrophobic force model through an experimental comparison of the kinetics of collision of particles against bubbles in flotation cells with the simulation results.     

基于有限元的缓冲包装结构参数对缓冲性能影响的仿真研究

传统的纸浆模塑缓冲包装结构的强度与极限承载能力分析是以实验研究为基础的,同时这也是结构研究的基本方法,但由于实验本身所存在的局限性,使结构设计的发展受到了某些限制.文中给出一种利用ANSYS软件对缓冲包装结构进行设计,为结构在各种不同设计参数下的极限承载能做出了分析和计算,为结构设计提供了理论依据.     

Parametric Analysis of Tensile Properties of Bimodal Al Alloys by Finite Element Method

An axisymmetrical unit cell model was used to represent a bimodal Al alloy that was composed of both nano-grained (NG) and coarse-grained (CG) aluminum. Effects of microstructural and materials parameters on tensile properties of bimodal Al alloy were investigated by finite element method (FEM). The parameters analyzed included aspect ratios of CG Al and the unit cell, volume fraction of CG Al (VFCG), and yield strength and strain hardening exponent of CG Al. Aspect ratios of CG Al and the unit cell have no significant influence on tensile stress-strain response of the bimodal Al alloy. This phenomenon derives from the similarity in elastic modulus and coefficient of thermal expansion between CG Al and NG Al. Conversely, tensile properties of bimodal Al alloy are extremely sensitive to VFCG, yield strength and strain hardening exponent of CG Al.Specifically, as VFCG increases, both yield strength and ultimate tensile strength (UTS) of the bimodal Al alloy decreases, while uniform strain of bimodal Al alloy increases. In addition, an increase in yield strength of CG Al results in an increase in both yield stress and UTS of bimodal Al alloy and a decrease in uniform strain of bimodal Al alloy. The lower capability in lowering the increase of stress concentration in NG Al due to a higher yield strength of CG Al causes the lower uniform strain of the bimodal Al alloy. When strain hardening exponent of CG Al increases, 0.2% yield stress, UT5, and uniform strain of the bimodal Al alloy increases. This can be attributed to the increased work-hardening ability of CG Al with a higher strain hardening exponent.     

Optimization of Johnson-Cook Constitutive Model for Lead-free Solder Using Genetic Algorithm and Finite Element Simulations

To ensure the reliability of microelectronics packages, the high strain rate deformation behavior of the solder joints must be properly understood. Accordingly, the present study proposes a hybrid experimental / numerical method for determining the optimal constants of the Johnson-Cook (J-C) constitutive model for 96.5Sn-3Ag-0.5Cu (SAC305) solder alloy. In the proposed approach, FEM simulations based on the J-C model are performed to describe the load-time response of an SAC305 ball solder joint under an impact velocity of 0.5 m/s. The optimal values of the constitutive model are then determined using an iterative Genetic Algorithm approach based on a comparison of the simulated load-time response and the experimental load-time response. The optimality of the optimized constants is demonstrated by comparing the experimental and simulation results for the load-time curves under impact speeds of 0.3 ∼ 1.0 m/s. It is shown that a good agreement exists between the two sets of results for all values of the impact speed. In other words, the results confirm the validity of the proposed hybrid approach as a means of evaluating the high strain-rate response of lead-free solder.     

An RMVT-Based Finite Rectangular Prism Method for the 3D Analysis of Sandwich FGM Plates with Various Boundary Conditions

A Reissner's mixed variational theorem (RMVT)-based finite rectangular prism method (FRPM) is developed for the three-dimensional (3D) analysis of sandwich functionally graded material (FGM) plates subjected to mechanical loads, in which the edge conditions of the plates are such that one pair of opposite edges is simply supported and the other pair may be combinations of free, clamped or simply supported edges. The sandwich FGM plate considered consists of two thin and stiff homogeneous material face sheets combined with an embedded thick and soft FGM core, the material properties of which are assumed to obey the powerlaw distributions of the volume fractions of the constituents. In this formulation, the plate is divided into a number of finite rectangular prisms, in which the trigonometric functions and Lagrange polynomials are used to interpolate the y-direction and x-ζ plane variations of the primary field variables of each individual prism, respectively. Because an h-refinement process is adopted to yield the convergent solutions in this analysis, the prism-wise either linear or quadratic function distribution through the x-ζ plane is assumed for the related field variables. A unified formulation of these FRPMs with freely-chosen orders for assorted field variables is presented. It is shown that these quadratic FRPM solutions of simply supported, multilayered composite plates and sandwich FGM ones are in excellent agreement with the exact 3D solutions available in the literature, and those of multilayered composite plates with various boundary conditions closely agree with the solutions obtained using the ANSYS commercial software.